Cardinality of a Set Worksheet/Game

Cardinality of a Set Worksheet/Game
Welcome to Cardinality of a Set Worksheet/Game. This game requires you to use the Principle of Inclusion-Exclusion and set logic to solve for missing values. Scroll down the page for a more detailed explanation.

 

 

How to Play

1. Analyze the “Givens”
   At the top of the game area, you are provided with a set of known values (the “Givens”). These usually include:
   n(U): The total number of elements in the Universal Set.
   n(A) and n(B): The total number of elements in each individual set.
   n(A ∩ B): The number of elements where the two sets overlap.
   

2. Solve the Challenge
   The main blue box will ask you to find a specific value, such as n(A ∪ B) (the total of both sets) or n(A’) (everything outside of A). You must calculate the number, type it into the input box, and hit SUBMIT.
   

3. Learn from Feedback
   Correct: You’ll get a green “Correct” message.
   Incorrect: The game will turn red and show you the specific formula you should have used to find that answer. This is a great way to learn the math as you play.
   

The “Cheat Sheet” for Success
To win this game, you need to know how the different regions of a Venn Diagram relate to each other.

Goal	Symbol	The Logic / Formula
Union	n(A ∪ B)	Add A and B, then subtract the overlap: n(A) + n(B) - n(A ∩ B)
Intersection	n(A ∩ B)	Add A and B, then subtract the Union: n(A) + n(B) - n(A ∪ B)
Complement	n(A')	Subtract the set from the total: n(U) - n(A)
A Only	n(A only)	Take the whole of A and remove the overlap: n(A) - n(n(A ∩ B))
Outside Both	n(A ∪ B)'	Subtract the Union from the total: n(U) - n(A ∪ B)

The Principle of Inclusion-Exclusion

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